Working Group in the History and Philosophy of
Logic, Mathematics, and Science

2016-17

November 02, 2016, 6-7:30 PM in 234 Moses Hall

Bernhard Nickel (Harvard University)

Predicativism and the Semantic Argument

Predicativism about names holds that proper names are fundamentally count nouns, a hypothesis most directly illustrated by examples like “there are two Alfreds at Princeton.” When names are used to refer to particular objects, they form complex noun phrases. On one prominent elaboration of the view, “Alfred is in the room” has roughly this logical form: “[The] Alfred is in the room”, where the square brackets indicate that the article is present in the logical form but unpronounced. This is a form of descriptivism that may make descriptivist treatments of long-standing puzzles about proper names available while being immune to Kripke’s challenges to descriptivism. Much of the literature has asked whether predicativism can answer Kripke’s modal argument, which turns on the claim that names are rigid designators. This paper focuses on Kripke’s semantic argument, which seeks to show that the reference of a proper name cannot be fixed by a description the speaker grasps (exemplified by the Godel/Schmidt case). I argue that predicativism falls prey to this objection, as well.

November 16, 2016, 6-7:30 PM in 234 Moses Hall

Juliette Kennedy (University of Helsinki)

Squeezing Arguments and Strong Logics

G. Kreisel has suggested that squeezing arguments, originally formulated for the informal concept of first order validity, should be extendable to second order logic, although he points out obvious obstacles. We develop this idea in the light of more recent advances and delineate the difficulties across the spectrum of extensions of first order logics by generalised quantifiers and infinitary logics. This is joint work with Jouko Väänänen.

February 08, 2017, 6-7:30 PM in 234 Moses Hall

Kevin T. Kelly and Konstantin Genin (Carnegie Mellon University)

An Epistemic Justification of Ockham’s Razor in Statistical Inductive Inference

Bayesian statistics allows for inductive inferences beyond the information provided, but it does not provide an epistemic justification in terms of finding the truth better than alternative methods. Frequentist methods come with epistemic guarantees, but the guarantees are too strong to allow for inductive inference. So there is currently no epistemic justification for inductive statistical inference of any kind; much less for Ockham’s razor. We will propose one. The idea is this. Everyone knows that deductive inference is monotonic, meaning that more premises never yield fewer conclusions. Inductive inference is non-monotonic. Everyone allows that deductive (monotonic) inference is better justified epistemically than inductive (non-monotonic) inference. So, presumably, more monotonicity is epistemically better than less. Our thesis is that optimally monotonic inference is necessarily Ockham inference. Before now, we have fully demonstrated that thesis only in the case of qualitative information. In this talk, we extend the result to statistical inference. The development will also illuminate broadly logical (i.e. topological) outlines in frequentist statistics that are crucial, but rarely emphasized.

February 22, 2017, 6-7:30 PM in 234 Moses Hall

Sean Walsh (Department of Logic and Philosophy of Science, UC Irvine)

Interpreting Categorical Grammar in Church’s Intensional Logic

Church’s intensional logic was an attempt to axiomatize the relation which a Fregean sense bears to a referent in the circumstance that there is a linguistic expression which expresses the sense and denotes the referent. In some recent work ([1]), fragments of Church’s intensional logic have been developed which resolve the paradoxes of propositions by weakening comprehension. In this talk, we survey these fragments and assay the extent to which the traditional Montagovian interpretation of categorical grammar into the intensional theory of types can be mirrored by a interpretation of categorical grammar into the fragments of Church’s intensional logic.

In the 19th century a handful of short difficult papers about solution methods for polynomial equations grew into a vigorous branch of algebra (Galois theory) and even into a rallying cry for modern structural mathematics. The influential German mathematician Felix Klein’s well-known but little-read book The Icosahedron of 1884 played a significant, and often neglected, role in the controversies that attended the creation of these ideas. The arguments he and his opponents used range over important questions about the organisation of mathematical knowledge and the direction of research.